Finite Group Databasebeta

← C11×#23591 #14600784

Subgroups — C11×#23591 #14600784

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3460C211yesmaximal, characteristic, complemented
2C4×C11×AGL(1,ℤ/8)C212yesmaximal, complemented
3C11×#2328C211yesmaximal, characteristic, complemented
4C11×#2061C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#2027C211yesmaximal, characteristic, complemented
8C11×#2006C211yesmaximal, characteristic, complemented
9C11×#2002C212yesmaximal, complemented
10C11×#1759C212yesmaximal, complemented
11C4×C11×#100C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2212yes—
13C11×#544C2211yescharacteristic
14C11×#542—22no—
15C11×#540—22no—
16C11×#538—22no—
17C11×#537C2211yescharacteristic
18C11×#535C2212yes—
19C11×#532—22no—
20C2×C11×#127C2211yescharacteristic
21C11×#529—22no—
22C11×#525—22no—
23C4×C11×#41C2212yes—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#442—22no—
27C11×#440—22no—
28C4×C11×SD16—22no—
29C4×C11×D8—22no—
30C11×#428C2212yes—
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#418C2212yes—
34C11×#417C2212yes—
35C2×C11×#100C2212yes—
36C4×C11×M16C2212yes—
37C11×#390C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#386—22no—
40C11×#386—22no—
41C11×#382C2211yescharacteristic
42C11×#376C2211yescharacteristic
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#339C2212yes—
46C11×#339C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41C2312yes—
49C22×D4×C11—22no—
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11D412yes—
54C11×AGL(1,ℤ/8)—24no—
55C11×AGL(1,ℤ/8)—24no—
56C2×C11×SD16—22no—
57C2×C11×D8—22no—
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C11×C4⋊Q8—22no—
61C11×#127—22no—
62C11×#127—22no—
63C11×#127—22no—
64C11×#126—24no—
65C11×#125—22no—
66C11×#124—24no—
67C11×#124—22no—
68C11×#123—24no—
69C11×#123—24no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×#121—22no—
74C11×#121—24no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#120—24no—
80C4×Q8×C11D412yescomplemented
81C4×Q8×C11D412yescomplemented
82C4×D4×C11—24no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11D412yescomplemented
90C4×D4×C11D412yescomplemented
91C11×#117—22no—
92C11×#117—22no—
93C11×#117C2312yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4D412yes—
100C2×C42×C11—22no—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C11×#107—22no—
105C11×#106—22no—
106C11×#104—24no—
107C11×#104—24no—
108C11×#103—22no—
109C11×#102—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#100—24no—
113C11×#97—22no—
114C4×C8×C11—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—22no—
118#23591C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C24×C11C2×D412yes—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—84no—
126C2×Q8×C11—22no—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—22no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—28no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—82no—
141C2×D4×C11—82no—
142C2×D4×C11C2×D412yes—
143C2×D4×C11#4112yescomplemented
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—42no—
153C22×C4×C11—82no—
154C22×C4×C11—82no—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C11×SD16—28no—
160C11×D8—28no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16#4114yescomplemented
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4C2×D412yes—
175C11×C4⋊C4C2×D412yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—82no—
186C11×C22⋊C4—82no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—21no—
191C42×C11—22no—
192C42×C11C2×D412yes—
193C42×C11C2×D412yes—
194C42×C11#4112yescomplemented
195#3460C2×C1111yescharacteristic, complemented
196C4×AGL(1,ℤ/8)C2×C1112yescomplemented
197#2328C2×C1111yescharacteristic, complemented
198#2061C2×C1111yescharacteristic, complemented
199#2040C2×C1111yescharacteristic, complemented
200#2037C2×C1112yescomplemented
201#2027C2×C1111yescharacteristic, complemented
202#2006C2×C1111yescharacteristic, complemented
203#2002C2×C1112yescomplemented
204#1759C2×C1112yescomplemented
205C4×#100C2×C1111yescharacteristic, complemented
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11C22×D411yescharacteristic
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—82no—
221D4×C11—22no—
222D4×C11—24no—
223D4×C11—22no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—84no—
230D4×C11—88no—
231D4×C11—82no—
232D4×C11—84no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—82no—
253C2×C4×C11—82no—
254C2×C4×C11—84no—
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12012yes—
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11C22×D412yes—
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4112yes—
261C2×C4×C11C2×#4111yescharacteristic
262C8×C11—24no—
263C8×C11—42no—
264C2×AGL(1,ℤ/8)C22×C1112yes—
265#544C22×C1111yescharacteristic
266#542—22no—
267#540—22no—
268#538—22no—
269#537C22×C1111yescharacteristic
270#535C22×C1112yes—
271#532—22no—
272C2×#127C22×C1111yescharacteristic
273#529—22no—
274#525—22no—
275C4×#41C22×C1112yes—
276C2×C4×D4C22×C1111yescharacteristic
277C2×C4×D4C22×C1111yescharacteristic
278#442—22no—
279#440—22no—
280C4×SD16—22no—
281C4×D8—22no—
282#428C22×C1112yes—
283C2×#104C22×C1112yes—
284C2×#104C22×C1112yes—
285#418C22×C1112yes—
286#417C22×C1112yes—
287C2×#100C22×C1112yes—
288C4×M16C22×C1112yes—
289#390C22×C1111yescharacteristic
290#390C22×C1111yescharacteristic
291#386—22no—
292#386—22no—
293#382C22×C1111yescharacteristic
294#376C22×C1111yescharacteristic
295#343C22×C1111yescharacteristic
296#343C22×C1111yescharacteristic
297#339C22×C1112yes—
298#339C22×C1112yes—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11C2×#12011yescharacteristic
315C22×C11#52511yescharacteristic
316C22×C11#53211yescharacteristic
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—22no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11#52512yes—
328C4×C11#53212yes—
329C2×#41—22no—
330C2×#41C23×C1112yes—
331C22×D4—22no—
332C22×D4C23×C1111yescharacteristic
333C22×D4C23×C1111yescharacteristic
334C23×C4—21no—
335C23×C4D4×C1112yes—
336AGL(1,ℤ/8)—24no—
337AGL(1,ℤ/8)—24no—
338C2×SD16—22no—
339C2×D8—22no—
340C2×M16C23×C1112yes—
341C2×M16C23×C1112yes—
342C4⋊Q8—22no—
343#127—22no—
344#127—22no—
345#127—22no—
346#126—24no—
347#125—22no—
348#124—24no—
349#124—22no—
350#123—24no—
351#123—24no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355#121—22no—
356#121—24no—
357#121—22no—
358#121—22no—
359#121—22no—
360#121—22no—
361#120—24no—
362C4×Q8D4×C1112yescomplemented
363C4×Q8D4×C1112yescomplemented
364C4×D4—24no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4D4×C1112yescomplemented
372C4×D4D4×C1112yescomplemented
373#117—22no—
374#117—22no—
375#117C23×C1112yes—
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4D4×C1112yes—
382C2×C42—22no—
383C2×C42C23×C1111yescharacteristic
384C2×C42C23×C1111yescharacteristic
385C2×C42C23×C1111yescharacteristic
386#107—22no—
387#106—22no—
388#104—24no—
389#104—24no—
390#103—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#100—24no—
395#97—22no—
396C4×C8—22no—
397#95—21no—
398#95—21no—
399#95—22no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—82no—
403C2×C11—82no—
404C2×C11—82no—
405C2×C11#238811yescharacteristic
406C2×C11#301911yescharacteristic
407C2×C11#302111yescharacteristic
408C24—21no—
409C24C2×D4×C1112yes—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—84no—
415C2×Q8—22no—
416C2×Q8C2×D4×C1112yes—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—28no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—82no—
430C2×D4—82no—
431C2×D4C2×D4×C1112yes—
432C2×D4C11×#4112yescomplemented
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4C2×D4×C1112yes—
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C24×C1111yescharacteristic
448SD16—28no—
449D8—28no—
450M16—22no—
451M16—22no—
452M16—22no—
453M16C11×#4114yescomplemented
454C2×C8—22no—
455C2×C8—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4C2×D4×C1112yes—
464C4⋊C4C2×D4×C1112yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—82no—
475C22⋊C4—82no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—21no—
480C42—22no—
481C42C2×D4×C1112yes—
482C42C2×D4×C1112yes—
483C42C11×#4112yescomplemented
484C11#2359111yescharacteristic, direct product factor, Sylow
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—41no—
495C23—41no—
496C23C22×D4×C1111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—82no—
500D4—22no—
501D4—24no—
502D4—22no—
503D4—42no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—84no—
509D4—88no—
510D4—82no—
511D4—84no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—84no—
534C2×C4C11×#12011yescharacteristic
535C2×C4C11×#12012yes—
536C2×C4C11×#12011yescharacteristic
537C2×C4C22×D4×C1112yes—
538C2×C4C2×C11×#4111yescharacteristic
539C2×C4C2×C11×#4112yes—
540C2×C4C2×C11×#4111yescharacteristic
541C8—24no—
542C8—42no—
543C22—21no—
544C22—21no—
545C22—44no—
546C22—44no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—82no—
555C22—82no—
556C22—81no—
557C22—81no—
558C22C2×C11×#12011yescharacteristic
559C22C11×#52511yescharacteristic
560C22C11×#53211yescharacteristic
561C4—21no—
562C4—21no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4C11×#52512yes—
572C4C11×#53212yes—
573C2—21no—
574C2—21no—
575C2—82no—
576C2—82no—
577C2—82no—
578C2C11×#238811yescharacteristic
579C2C11×#301911yescharacteristic
580C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3460C2semidirect
2. C4×C11×AGL(1,ℤ/8)C2semidirect
3. C11×#2328C2semidirect
4. C11×#2061C2semidirect
5. C11×#2040C2semidirect
6. C11×#2037C2semidirect
7. C11×#2027C2semidirect
8. C11×#2006C2semidirect
9. C11×#2002C2semidirect
10. C11×#1759C2semidirect
11. C4×C11×#100C2semidirect
80. C4×Q8×C11D4semidirect
81. C4×Q8×C11D4semidirect
89. C4×D4×C11D4semidirect
90. C4×D4×C11D4semidirect
118. #23591C11direct (N × H)
143. C2×D4×C11#41semidirect
164. C11×M16#41semidirect
194. C42×C11#41semidirect
195. #3460C2×C11semidirect
196. C4×AGL(1,ℤ/8)C2×C11semidirect
197. #2328C2×C11semidirect
198. #2061C2×C11semidirect
199. #2040C2×C11semidirect
200. #2037C2×C11semidirect
201. #2027C2×C11semidirect
202. #2006C2×C11semidirect
203. #2002C2×C11semidirect
204. #1759C2×C11semidirect
205. C4×#100C2×C11semidirect
362. C4×Q8D4×C11semidirect
363. C4×Q8D4×C11semidirect
371. C4×D4D4×C11semidirect
372. C4×D4D4×C11semidirect
432. C2×D4C11×#41semidirect
453. M16C11×#41semidirect
483. C42C11×#41semidirect
484. C11#23591direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#34602
C4×C11×AGL(1,ℤ/8)2
C11×#23282
C11×#20612
C11×#20402
C11×#20372
C11×#20272
C11×#20062
C11×#20022
C11×#17592
C4×C11×#1002
#2359111